IST is a meridian of longitude. It is at a distance of 82.5° from the Greenwich towards the EAST. It passes through ALLAHABAD which is the approximate centre of India.
This meridian of longitude (82.5°E) is 5 and a half hours ahead from the time at Greenwich. India has the IST as it's standard time because if it wouldn't have been there, the country would have difference of 2 hours (as India is a large country and has a large East-west extent --- there's a difference of 2 hours from Gujarat in the west to Assam in the east). Hence, IST is an important meridian of longitude.